{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f853457a6a0>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from DistantSpeech.beamformer.utils import load_audio as audioread\n",
    "from DistantSpeech.beamformer.utils import save_audio as audiowrite\n",
    "from DistantSpeech.transform.multirate import frac_delay\n",
    "delta = 2.5\n",
    "N = 128\n",
    "w_max=0.9\n",
    "C=4\n",
    "\n",
    "# constraints\n",
    "N_C = int(C * N)\n",
    "w = np.linspace(0, w_max * np.pi, N_C)[:, np.newaxis]\n",
    "\n",
    "n = np.arange(N)\n",
    "\n",
    "try:\n",
    "    from cvxopt import solvers, matrix\n",
    "except:\n",
    "    raise ValueError(\n",
    "        \"To use the frac_delay function, the cvxopt module is necessary.\"\n",
    "    )\n",
    "\n",
    "f = np.concatenate((np.zeros(N), np.ones(1)))\n",
    "\n",
    "A = []\n",
    "b = []\n",
    "for i in range(N_C):\n",
    "    Anp = np.concatenate(\n",
    "        ([np.cos(w[i] * n), -np.sin(w[i] * n)], [[0], [0]]), axis=1\n",
    "    )\n",
    "    Anp = np.concatenate(([-f], Anp), axis=0)\n",
    "    A.append(matrix(Anp))\n",
    "    b.append(\n",
    "        matrix(np.concatenate(([0], np.cos(w[i] * delta), -np.sin(w[i] * delta))))\n",
    "    )\n",
    "\n",
    "solvers.options[\"show_progress\"] = False\n",
    "sol = solvers.socp(matrix(f), Gq=A, hq=b)\n",
    "\n",
    "h = np.array(sol[\"x\"])[:-1, 0]\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "w = np.linspace(0, np.pi, 2*N_C)\n",
    "F = np.exp(-1j*w[:,np.newaxis]*n)\n",
    "Hd = np.exp(-1j*delta*w)\n",
    "plt.figure()\n",
    "plt.subplot(3,1,1)\n",
    "plt.plot(np.abs(np.dot(F,h) - Hd))\n",
    "plt.subplot(3,1,2)\n",
    "plt.plot(np.diff(np.angle(np.dot(F,h))))\n",
    "plt.subplot(3,1,3)\n",
    "plt.plot(h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = audioread('/home/wangwei/work/DistantSpeech/samples/audio_samples/cleanspeech_aishell3.wav')\n",
    "h1 = frac_delay(2, 40, w_max=0.9, C=4)\n",
    "h2 = frac_delay(3, 40, w_max=0.9, C=4)\n",
    "h3 = frac_delay(3.5, 40, w_max=0.9, C=4)\n",
    "out1 = np.convolve(data, h1)\n",
    "out2 = np.convolve(data, h2)\n",
    "out3 = np.convolve(data, h3)\n",
    "audiowrite('aec/out1.wav', out1)\n",
    "audiowrite('aec/out2.wav', out2)\n",
    "audiowrite('aec/out3.wav', out3)"
   ]
  }
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